Negative refraction index metamaterials and their predicted effects have been theoretically studied, numerically analyzed, and experimentally demonstrated from microwaves to light by many researchers in the past decade. See V. G. Veselago and E. E. Narimanov, Nature Materials 5, 759 (2006). However, anisotropy, dispersion, high refractive index contrast, and particularly loss make the adoption of existing designs to the optical regime difficult without adding gain. See J. Valentine et al., Nature 455, 376 (2008); and S. Xiao et al., Nature 466, 735 (2010). In particular, conventional approaches for obtaining metamaterial properties (±∈r, ±μr) are based on orientation dependent, lossy metallic structures, e.g., split-ring resonator/wire pairs, fishnet and omega shaped structures. However, metamaterials comprising metallic resonators have high conduction loss and have a detailed geometry which is difficult to fabricate on a micron scale required for use at infrared and optical frequencies. Further, a metamaterial with isotropic negative permeability would require three orthogonal orientations of split-ring resonators.
An alternative route, via Mie resonances of magnetodielectric structures, provides a mechanism for engineered electrical and magnetic response. In particular, an all-dielectric metamaterial is easier to fabricate at RF to optical wavelengths, and can have a higher efficiency than metallic metamaterials because of not having metallic loss. In addition, an isotropic metamaterial can be achieved using dielectric spheres. Therefore, to achieve low-loss 3D isotropic scattering at very high frequencies, the unit cell or building block of the negative index material can be a directional independent non-metallic scatterer. For example, double negative (DNG) materials are man-made crystals, wherein the lattice configuration and unit-cell geometry affect scattering, and wherein the effective permeability and permittivity of the crystal can be simultaneously negative for wavelengths where the scatterers are resonant. The ideal directionally independent scatterer is a dielectric sphere. Cubic lattices of dielectric spheres have been predicted to exhibit the DNG property if the unit-cell contains a single sphere with similar relative permittivity and permeability embedded in an air-like host medium. See C. L. Holloway et al., IEEE Trans. on Antennas and Propagation 51, 2596 (2003). However, low-loss isotropic materials with scalar negative permittivity and permeability (or negative index of refraction) are straightforward to analyze, yet rather difficult to realize.
Another drawback to this approach is the simultaneous requirement on the permittivity and permeability. Because permeability greater than unity is difficult to obtain with low loss near optical frequencies, several researchers have proposed the two-sphere per unit cell approach. Spheres of different sizes or of the same-size but with different permittivities may be placed next to each other so that their electric and magnetic resonances overlap. See O. G. Vendik and M. S. Gashinova, Proc. 34th European Microwave Conference 3, 1209 (2004); and A. Ahmadi and H. Mosallaei, Phys. Rev. B 77, 045104 (2008). However, these designs are not strictly isotropic. See I. Vendik et al., Microwave and Optical Technology Letters 48, 2553 (2006). Another approach to isotropy is to develop bi-layered concentric spheres, commonly referred to as the core-shell structure. See E. F. Kuester et al., A double negative (DNG) composite medium based on a cubic array of layered nonmagnetic spherical particles, URSI 2007—CNC/USNC North American Radio Science Meeting, Ottawa, Canada, 2007. For the core-shell configuration, the key difficulty is numerical optimization. Another approach to DNG 3D isotropy at low-frequencies (L-band) uses artificial transmission lines loaded with reactive lumped elements. See A. Grbic and G. V. Eleftheriades, J. Appl. Phys 98, 043106 (2005). The key difficulties have been design optimization, material selection, and manufacturability.
Therefore, a need remains for a resonant dielectric metamaterial that is isotropic, easy to manufacture, and can be used to develop Ku/K band systems.